On the spaces of $\lambda -$ convergent and bounded series

Abstract

The main purpose of this study is to introduce the spaces $c{s}^{\lambda },c{s}_0^{\lambda }$ and $b{s}^{\lambda }$ which are $BK-$spaces of non-absolute type. We prove that these spaces are linearly isomorphic to the spaces $cs,c{s}_0$ and $bs$, respectively and derive some inclusion relations. Additionally, their Schauder bases have been constructed and the $\alpha -,\beta -$ and $\gamma -$ duals of these spaces have been computed. Finally, we characterize some matrix classes from the spaces $c{s}^{\lambda },c{s}_0^{\lambda }$ and $b{s}^{\lambda }$ to spaces ${\ell }_p,c$ and $c_0$, where $1\le p\le \infty$ .

arXiv comment15 pages research article